The invention is based on an air flow rate meter as defined generally hereinafter. An air flow rate meter is already known (German Offenlegungsschrift 27 50 050) in which deposits occur on the surface of the temperature-dependent resistor, which is embodied as a hot wire, when it is used for measuring the mass of air aspirated by an internal combustion engine. As a result, the accuracy and speed of the measurement are both impaired. In this known air flow rate meter, it is accordingly provided that at certain times, for instance immediately after the ignition has been shut off, a burn-off procedure is performed, during which the deposits on the temperature-dependent resistor burn off as a result of an increase in the temperature of the resistor brought about by supplying a higher current to it. However, in so doing it cannot be precluded that a rich fuel-air mixture may be located in the intake tube in the vicinity of the temperature-dependent resistor and as a consequence may then ignite at the red-hot resistor during the burn-off procedure, especially under the catalytic influence of a temperature-dependent resistor fabricated from platinum wire. The result is a further, undesirable increase of temperature at the temperature-dependent resistor, which may cause the destruction of the temperature-dependent resistor.